Information-theoretic aspects of Werner states

Journal Article · Fri Jan 15 04:00:00 EST 2021 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2020.168371· OSTI ID:23183265

Li, Nan; Luo, Shunlong ^[1]; Sun, Yuan ^[2]

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1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023 (China)

Highlights: • The rich structures of Werner states are reviewed. • Werner states are characterized in terms of quantum uncertainty. • Information-theoretic aspects of Werner states are revealed. In a seminal study of quantum states with Einstein–Podolsky–Rosen correlations (entanglement) admitting a hidden-variable model (Werner, 1989), Werner introduced the dichotomy of entanglement/separability and devised a family of highly symmetric states, now termed the Werner states, some of which exhibit entanglement but no Bell nonlocality. It turns out that the Werner states have a rich structure of correlations and constitute a paradigm which has played an innovative role in both theoretical and experimental explorations of quantum information. Given the theoretical significance and wide applications of the Werner states, here we first give a concise review of information contents of the Werner states, and then present an information-theoretic characterization of them in terms of the Wigner–Yanase skew information: The Werner states are identified as the states with the minimum quantum uncertainty with respect to a natural family of observables (i.e., the generators of the diagonal unitary group). For this purpose, we introduce a measure of quantum uncertainty which is of independent interest in studying asymmetry, coherence, and uncertainty, and reveal its fundamental properties. We further identify the Bell triplet states as the opposite states of the Werner states in the sense that they have the maximal amount of quantum uncertainty. Analogously, we provide a similar characterization of the isotropic states as the minimum quantum uncertainty states with respect to a closely related family of operators.

• OSTI ID: 23183265
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 424; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMMETRY
EXPLORATION
HIDDEN VARIABLES
QUANTUM ENTANGLEMENT
QUANTUM INFORMATION
QUANTUM STATES
SYMMETRY
TRIPLETS